Problem: Gabriela is 3 times as old as Omar. Ten years ago, Gabriela was 5 times as old as Omar. How old is Gabriela now?
Solution: We can use the given information to write down two equations that describe the ages of Gabriela and Omar. Let Gabriela's current age be $g$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $g = 3o$ Ten years ago, Gabriela was $g - 10$ years old, and Omar was $o - 10$ years old. The information in the second sentence can be expressed in the following equation: $g - 10 = 5(o - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to solve our first equation for $o$ and substitute it into our second equation. Solving our first equation for $o$ , we get: $o = g / 3$ . Substituting this into our second equation, we get: $g - 10 = 5($ $(g / 3)$ $- 10)$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $g - 10 = \dfrac{5}{3} g - 50$ Solving for $g$ , we get: $\dfrac{2}{3} g = 40$ $g = \dfrac{3}{2} \cdot 40 = 60$.